Docs: Refactor dependency injection examples with inject() function - Issue 23270

[fahrigedik]

Description

⚠️ Will be on draft until we published this :: #23262

Resolves #23270 (write the related issue number if available)

TODO: This PR updates the Angular documentation to use the modern inject() function for dependency injection instead of constructor-based injection.

Changes include:

• Replaced constructor injection examples with inject() usage.
• Updated code snippets and explanations to align with Angular 14+ best practices.
• Improved clarity and consistency in DI-related sections.

This ensures our docs stay up-to-date with the latest Angular DI patterns and help developers adopt the new API more easily.

[sumeyyeKurtulus]

It looks pretty nice and neat apart from very small points. If we just resolve the comments and these notes, it is ready to be merged

• We need to change this constructor injection either

  docs/en/framework/ui/angular/theming.md

  constructor(@Inject(INJECTOR_PIPE_DATA_TOKEN) public data: UserMenu) {}

• That would be the best if we also update these. Even if they are not listed in the navigation bar, they are still reachable.

  • docs/en/framework/ui/angular/how-replaceable-components-work-with-extensions.md

  • docs/en/framework/ui/angular/http-error-reporter-service.md

  • docs/en/framework/ui/angular/permission-management-component-replacement.md

  • docs/en/modules/setting-management.md

  • docs/en/ui-themes/lepton-x/angular-customization.md

  • the same applies for the tutorials folder :: docs/en/tutorials